JPH02190704A - Method for determining incident angle in refractive index/film thickness measurement - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to a method for specifying an angle of incidence in measuring refractive index and film thickness.

[Prior Art] Ellipsometry has been known as a method for measuring the refractive index and film thickness of thin films.

[Problems to be Solved by the Invention] Although ellipsometry is a highly accurate measurement, the accuracy may be extremely poor depending on the membrane being measured.

Such a region where the accuracy deteriorates can be avoided by changing the incident angle. However, in the past, it was not possible to know in advance what incident angle should be selected in order to obtain good measurement accuracy, and it was necessary to find the appropriate incident angle by trial and error.

Therefore, the inventor proposed a method of identifying in advance the angle of incidence at which the measurement accuracy deteriorates (Japanese Patent Application No. 62-192396).
issue). However, this method can only be applied to the measurement of the refractive index and film thickness of a single layer film formed on a substrate with a known complex refractive index, and the light used for measurement is also limited to S-polarized light.

The present invention has been made in view of the above-mentioned circumstances, and its purpose is to improve measurement accuracy when implementing measurement methods such as ellipsometry for measuring the refractive index and film thickness of thin films. An object of the present invention is to provide an incident angle determining method that can easily determine the incident angle.

[Means for Solving the Problems] The present invention will be described below. Two methods of determining the angle of incidence are proposed herein.

The method of claim 1 comprises: “known complex refractive index n*2=2−1
The refractive index of a single-layer thin film formed on a substrate with k2
A method for determining the measurement incident angle of monochromatic light for measurement when measuring film thickness, and has the following characteristics.

Various angles of incidence θ of monochromatic light of wavelength λ used for measurements. The energy reflectance Rs (θ0) or Rp (θ0) of S-polarized light or P-polarized light by the measurement sample is measured.

On the one hand, the substrate has a refractive index n. Energy reflectance of S-polarized light or P-polarized light when the monochromatic light is incident in the incident medium of 1 ro2s(it0)12 or l
ro2s(flo) l 2 is the incident angle θ using the above n; and no.

Calculated by calculation as a function of Then, an angle 6.0 that satisfies the equation % is determined, and this angle other than θ4° is defined as the measurement incident angle.

The method of claim 2 is characterized in that “known complex refractive index n:=n−1k
The refractive index of a thin film formed on a substrate formed by laminating one or more thin films of known refractive index and film thickness on a substrate having a
A method for determining the measurement incident angle of monochromatic light for measurement when measuring film thickness, and has the following characteristics.

Various angles of incidence θ of monochromatic light of wavelength λ used for measurements. The energy reflectances Rs (θ0) and Rp (θ0) of S-polarized light and P-polarized light by the measurement sample are measured.

On the one hand, the substrate has a refractive index n. The energy reflectance of S-polarized light and P-polarized light Rsbs (6o) and R8b11 (θ0
) and the incident angle θ using the above n: + n O and the known refractive index and film thickness of each thin film of the substrate. Calculated by calculation as a function of Then, the angle θ that simultaneously satisfies the equation %(0). . is determined, and this angle other than 6.0 is defined as the measured incident angle.

As described above, the method of claim 1 determines the "measurement angle of incidence" when measuring the refractive index and film thickness of a single-layer thin film formed on a "substrate" having a known complex refractive index. It's a method. The "measurement angle of incidence" is, needless to say, the angle at which monochromatic light is made incident on the measurement sample in order to measure the refractive index and film thickness. In determining the measurement incident angle, monochromatic light having the same wavelength as that used for measurement is used, but either S-polarized light or P-polarized light may be used.

The method of claim 2 is a method of determining a measurement incident angle when measuring the refractive index and film thickness of a thin film formed on a "substrate". The "substrate" is one in which one or more thin films with a known refractive index and film thickness are formed on a "substrate J having a known complex refractive index. Therefore, in the method of claim 2, A plurality of thin films are formed on a "substrate", and the refractive index and film thickness are measured for the topmost thin film among the plurality of thin films on the substrate.

In the method of claim 2, monochromatic light of S-polarized light and P-polarized light is used to determine the measurement incident angle as described above.

In addition to the above-mentioned ellipsometry, methods for measuring the refractive index and film thickness of thin films are also available.
The method proposed in No. 48742 (hereinafter referred to as P for convenience)
The present invention can be applied not only to ellipsometry but also as a method for determining the angle of incidence in the PRETTI method.

[Function] The principle of the method of claim 1 will be explained below with reference to FIG.

In FIG. 1, reference numeral 10 indicates a substrate, and reference numeral 12 indicates a transparent thin film. The substrate 10 has a known complex refractive index n*2
=2+ik2. The refractive index n1 and film thickness d of the thin film 12 are objects to be measured and are unknown. No represents the refractive index of the incident medium (generally the incident medium is air, so n may be set to 1).

Monochromatic light of wavelength λ is incident at angle θ. When incident on the thin film 12
, the refraction angle within the substrate 10 is set to θ1. Let it be θ2.

Here, for convenience of the following calculation, L2"TI't kffi +72"212 is 2+
2ui・ε2−n3sin2θO+((E2 nas
in2θ) 2172) 1/22v many knees (ε2-nos
in2θ, ) + ((ε2-n 5 in 2θ0) 2,000) 1″ to obtain n'22.n2cosθ2, n:2=
Rewrite it as ε,, iyz, n, cos θ2=u2+iV2.

When the thin film 12 is irradiated with monochromatic light as described above, P polarized light and S
The complex amplitude reflectances rp and rS of polarized light are each expressed as follows.

rp”(ro+p+r+2p'eXp(2iβ1))/
(1”ro+r・r+2p・exp(2iβI)
(1-1)rs"(robs"r+2s-eXp(2
iβ1))/(1+r.,,・r1□8・exp(2i
β, ) (1-2) P, S in the suffix
indicates that it relates to P-polarized light and S-polarized light. ,
razl and robs are Fresnel reflection coefficients for P and S polarized light at the interface between the incident medium and the thin film 12, and r
l 21'+ r l □5 is the Fresnel reflection coefficient for P and S polarized light at the interface between the thin film 12 and the substrate 10, and 2β is the Fresnel reflection coefficient for one round trip between the front and back surfaces of the thin film 12. This is the change in phase that occurs. These are expressed as follows.

ro+r”(n+cOsθ(,-n1cosθ+)/(
n, cosθo+nocosθ1)robs”(n1c
osθ+−n1cosθ+)/(nocosθo+n1
cOsθ1)r 12 P” (n Hcosθ+-n
+cosB)/(nHcosθ, +n, cos
θ;)r, 25:(n, cos6.-n", cos θ'
:)/(r++cosθ, +n1cosθ;)2β,=
4xd, (n4-sin2θ0)I/2/λ
(4) Also, since r1□P+'125 is generally a complex quantity, r+zp=j'+2peXp(lΦ+zp), r
+zsp+2seXI)(1Φ]2S), then ρ1
□2. ρI 2S+Φ12r+Φ125 is expressed as follows.

p721.・Re2(r+2p)”1m2(++ 2p
) (5-1) ρ725・Re2(r+zs)
+lm2(r+□s) (51)Φ,□
, +=tan-' (Im(r, 2.)/Re(r,
□1. Month (6-1)Φ+□5=tan-'(Im(
r+zs)/Re(r12s)) (6-2) However, Re(r+zp)=(+)+'p3"pz'p4)/
(p familiar "p#) Im(r+□p)・(1)2・p3-p
+・p4)/(p i + p fang), pl: ε2ul + γ2VI − ε1u2 − γIV2p22
ε2V1−了2ul−εIV2+Ding1u2p3”Z2u
+102V++1lu2+γIV2p2:ε2Vl−2ul+εIV2−γIu2, Re(rows): St/53 II(rows)”Sz/Sa, Sx”u+−u2÷vl−v2 S2”2(u2V+−u+V2) S3 "(u+"uz)"+(V1+V2)".

Based on (1-1) and (1-2), energy reflectance Rp.

Calculating Rs, Rp=(rf!+ll”27M+1÷2rou, p+
zpcos(Φ12r"2βl))/(1+Il'+
p p? ap ÷2ro lll II 12 pc
Os (Φ121"2 β direct)) R5"(r61s"P
Yvs”2ro r spr 2scOs(Φl 2S
”2β1))/(1+rgts11?zs+2ro+g
J++! 5CO8 (φ+2s”2β1)).

Here, 2β1 in (4) is 2β+=2mg (m=0.l, 2,3.,,)
An incident angle θ that satisfies (8). Considering (7-1), (2-1), (5-1), (6
-1) and (8), Rp becomes as follows.

Rp=((ni+ki)”cosg6+ng(u:
+vi)-2nocos6o(tzuz-γ2V2))
/((n number 10th) 2cos 2θ.+nro(U +V
)+2noCO8θ0((2u2−2V2))
(9-1) Also, (7-2) (2-
2), (5-2), (6-2), and (8), Rs becomes as follows.

Rs=((nocos6o-uz)2+vmulti)/((n
ocosθO+u2)”V poly) These (9-1), (
9-2) does not include the refractive index nl and film thickness d of the thin film 12.

Also, consider the case where there is no thin film 12 on the substrate 10 in FIG. 1, and let monochromatic light of wavelength λ be directly incident on it from the incident medium (refractive index n0) at an incident angle θ6. The energy reflectance for P-polarized light and S-polarized light is 1 r
021' I 2+ I rl12s 12 are respectively I r02P l ” 1 (n, cosθo−nQcOsθ1) vann1CO
Sθ(,+nocosθI)12((n multi-tenths)2co
s(io÷n: (ui+v)-2n, cosθo(ε
2u,, - completed2v2))/((n+nimany)2cos2
θo”no(ui”vM)”2n(, cosθ0(ε2
u2-d2V2)) (10-1)
rozs I ” (nocosθo-n, cosθ,)/(n, cosθ
(,+n1cosθ1)12”((nacosθ.-u
z)2+vto)/((n, cosθo+u2)2+vmultiple), which are (9-1) and (9
-2) is equal to Rp and Rs.

This means that the incident angle θ satisfies equation (8).

When monochromatic light is incident on the thin film 12 in This means that the energy reflectances Rp and Rs become equal to the energy reflectance of the substrate 1o alone given in (10-1) and (10-2) above. Therefore, at such a special angle of incidence, thin l! When light is incident on +2, it is theoretically impossible to know the refractive index and film thickness of the thin film 12 even if the energy reflectance is measured.

Such a special angle of incidence, ie, an angle of incidence that satisfies equation (8), will hereinafter be referred to as a singular angle of incidence and expressed as 0.0.

Therefore, when measuring the refractive index and film thickness of the thin film 12 by ellipsometry or the PRETTI method, an incident angle other than the above-mentioned singular incident angle may be used as the measurement incident angle.

To find out the singular angle of incidence, do the following: That is, as mentioned above, at a singular angle of incidence, for P polarized light, Rp'' l ro2p l 2 (111) becomes,
For S-polarized light, Rs=l rozs l 2(11-2),
The quantities on the left side of these (11-1) and (11-2) can be found by actually irradiating the thin film 12 with light and measuring its energy reflectance. On the other hand, the quantity on the right side is
Since the complex refractive index of the substrate 10 and the refractive index of the incident medium are known, if the incident angle is given, (10-1), (10-2
) can be calculated by calculation.

Therefore, when "measuring the refractive index and film thickness of a single-layer thin film formed on a substrate with a known complex refractive index n*2=2-ik2", it is necessary to use monochromatic light of wavelength λ used for measurement. Energy reflectance Rs(θ0) or R of S-polarized light or P-polarized light by the measurement sample for various incident angles θ0
p(θ0) and, on the other hand, the refractive index n of the substrate. Energy reflectance of S-polarized light or P-polarized light when the above monochromatic light is incident in an incident medium of 1 rozs
(flo) l 2 or j r62s ([10)
l 2 as the incident angle θ using the above n:, n,). Calculated by calculation as a function of and the singular angle of incidence θ, which satisfies the equation %). Find this θ. . It is sufficient to use an angle other than that as the measurement incident angle.

As is clear from the above description, either P-polarized light or S-polarized light may be used in carrying out the method of claim 1.
In the case of P-polarized light, Brewster's angle exists, and in addition to the case where formula 8) is satisfied, the incident angle is the Brewster's angle at the interface between the incident medium and the thin film, that is, l roIP I2
・Since the above equation (11-1) holds even when O, it may be difficult to find the singular angle of incidence in such cases, and considering this point, it is better to use S-polarized light. .

Next, the method of claim 2 will be explained with reference to FIG. 4 and subsequent figures.

In FIG. 4, m (≧2
) layer of thin film 22-1.22-2. , , , 22-m
is formed. The thin film 22-1 is the uppermost thin film, and the thin film 22-m is a thin film formed directly on the substrate 20.

As in FIG. 1, the refractive index of the incident medium is set to no, and the refractive indices of the thin films 22-1 to 22-m are sequentially changed to n1 as shown in the figure.
．． nH, n: +, , n2, film thickness sequentially dl+d2+
6. −*dm.

Note that the thin film 22-1 is transparent, and the thin films 22-2 to 22-
The refractive index of m is a complex refractive index. Further, it is assumed that the complex refractive index of the substrate 20 is n:=n, -ika. Complex refractive index nLn
L, -, n2 and n: are known and the film thickness d2. d...
, ,d, , are also known. Refractive index n1 of thin film 22-1
and the film thickness d+ are objects to be measured and are unknown. Therefore, the substrate 20 and the thin films 22-2 to 22-m constitute a "substrate",
It can be said that a thin film 221 is formed on this base.

As shown in Figure 4, in such a multilayer thin film, the wavelength λ
The monochromatic light has an incident angle θ. The complex amplitude reflectances r, , rs of P-polarized light and S-polarized light when the light is incident can be expressed as follows.

rr=(ro++−+r'pexp(2iβ1))/(
1+r. +pr',exp(2iβ,))(12-1)
rs: (rol s+r'5exp(2iβ1))/(
1"ro+sr'5exp(2iβ+))(12-2)
Here, ro1P+'OIS is the amplitude reflectance of P-polarized light and S-polarized light at the interface between the incident medium and the thin film 22-1, and r'll and r5 have the same refractive index as the thin film 22-1. represents the amplitude reflectance when the monochromatic light is incident on the "substrate" in the incident medium. Similarly to equation (4), 2β1 represents the phase change that occurs while the light travels back and forth between the front and back surfaces of the thin film 22-1.

The amplitude reflectance when multiple thin films are formed on the substrate 20 is as follows by comparing (12-1) and (12-2) with (11) and (1-2). As is clear, (12-1) and (12-2) are respectively (1-2
), In (1-2), r1□,.

, rl 25 is replaced by rl·+r'S.

Therefore, the angle of incidence, ie, the singular angle of incidence θ, that satisfies the above-mentioned equation (8). In the case of , the refractive index and film thickness of the thin film 22-1 are canceled and disappear from the formula expressing the energy reflectance, and Rp=Rsbr (13-
1) R3”Rsbs (1
3-2) holds true.

Here, the light enters R5bP+R8, or the "substrate", that is, the remaining part excluding the top layer thin film, at an incident angle θ. P when incident at
, is the energy reflectance of S-polarized light.

Therefore, in the method of claim 2, "known complex refractive index n*
When measuring the refractive index and film thickness of a thin film formed on a substrate formed by laminating one or more thin films of known refractive index and film thickness on a substrate having a = na - ika, the measurement Various angles of incidence θ of monochromatic light of wavelength λ used for against,
The energy reflectance Rs (θ0) and Rp (θ0) of S-polarized light and P-polarized light by the measurement sample were measured (13-1
), find the left-hand side of (13-2), and on the other hand,
The above substrate has a refractive index n. Energy reflectance R of S-polarized light and P-polarized light when the above monochromatic light is incident in the incident medium of
sbs(fl0) and Rsbp(θ0) above n:+
the incident angle θ using the known refractive index and film thickness of each thin film of the substrate. Calculated by calculation as a function of (13
-1), find the right side of (13-2).

And an angle θ that simultaneously satisfies equations (13-1) and (13-2). Find this singular angle of incidence θ,. An angle other than that may be determined as the measurement incident angle.

Incidentally, in both the inventions of claims 1 and 2, the calculations may be performed automatically by a computer programmed in advance.

[Example〕 Hereinafter, description will be given based on specific examples.

FIG. 13 schematically shows only the main parts of an apparatus for measuring the refractive index and film thickness of a thin film by the PRETTI method.

Light source 1 is a He-Ne laser with a wavelength of 6328A.

The light from this light source 1 is split into two by a beam splitter 2,
One side is guided to a photodetector 4 for photoelectric conversion. The other light is converted into S-polarized light or P-polarized light by the polarizer 3 and is made incident on the sample O.

Sample O is placed on the turntable 6.

The turntable 6 is rotated by an arm 7, and as shown in the figure, when the arm 7 rotates θ, the turntable 6 rotates 28 times. A photodetector 5 is fixed to the tip of the arm 7, and is capable of photoelectrically converting light reflected by the sample. By doing this, any incident angle θ to the sample O
(050590 degrees) can be measured.

The outputs of the photodetectors 4 and 5 are input to a data processing system 8 including a computer, and are subjected to arithmetic processing by the processing system 8.

In advance, the light amount ratio between the incident light and the light incident on the photodetector 4 is measured and input to the data processing system 8.

Now, as an example, in order to make it easier to understand the present invention, a simulation example will be explained for each method of claim 1.2, and finally, an example for the method of claim 1. Here is one example.

Example 1 (Embodiment of the invention of claim 1) As the substrate 10 in FIG. 1, n:i=3.858-0.01
Assuming a Si substrate of 8i, a thin film 12 is formed on this substrate with a refractive index of n.

Assume that =1.460, film thickness d, and =6328 people. Of course, in situations where the present invention is actually applied, the above nI
+ d1 is an unknown quantity to be measured, and the present invention is carried out to specify the angle of incidence for measuring these objects. A simulation will be used to explain how to determine the measurement incident angle of the invention. In addition, the incident medium is air. :1.

A laser beam with a wavelength of 6328A is incident on the thin film 12,
When the energy reflectance Rs of S-polarized light is calculated as a function of the incident angle according to equation (7-2) when the incident angle is continuously changed in the range of 0 to 90 degrees, the solid line in Figure 2 is obtained. becomes. When actually measuring the refractive index and film thickness of the thin film 12, this Rs is given as an actual measurement value.

On the other hand, when the energy reflectance 1 ro2s I' of S-polarized light when the above light is directly incident on the substrate IO in an air layer is calculated as a function of the incident angle according to (10-2),
The result is something like the broken line in FIG.

From FIG. 2, it can be seen that the singular angle of incidence that satisfies Rs=l r02s I'' is 44.2 degrees.

Therefore, the measurement incident angle may be set to an angle other than 42.2 degrees.

If we perform the same simulation as above for P polarized light instead of S polarized light, we get Rp, l rozp l
2 are as shown by solid lines and broken lines in FIG. 3, respectively. The equation Rs・l r02s l 2 holds in addition to the singular angle of incidence of 44.2 degrees, as well as the Brewster angle of 5
5.6 degrees, and in this situation it is difficult to unambiguously define the singular angle of incidence.

Example 2 (Example of the invention of claim 2) The same Si substrate (ns=3.858-0.018i) as the substrate of Example 1 is assumed as the substrate 20 in FIG. Rate n”, = n2 = 2.000, film thickness 800
The substrate provided with the 0A thin film is referred to as the "substrate". Then, on this substrate, refractive index n1=1.460, film thickness d1=7
Assume that a thin film is being formed to measure 400 people. Of course, let n(, = 1. ooo.

When a laser beam with a wavelength of 6328A is incident on such a measurement sample, the energy reflectance Rs of S-polarized light is determined by the incident angle (0
90 degrees), it becomes something like the solid line in FIG.

On the other hand, when the energy reflectance R8bS of S-polarized light is calculated as a function of the incident angle when the light is directly incident on the substrate in the air, it becomes as shown by the broken line in FIG.

The angle of incidence for RS”Rsbs is 33.1 degrees, 44
．． 2 degrees, 60.3 degrees.

The energy reflectance Rp of P-polarized light when a laser beam with a wavelength of 6328 people is incident on the measurement sample is determined by the incident angle (0 to
90 degrees), it becomes something like the solid line in FIG.

Further, when the energy reflectance R8b11 of P-polarized light is calculated as a function of the incident angle when the above-mentioned light is directly incident on the substrate in the air, it becomes as shown by the broken line in FIG. 6.

The incident angle where Rp=Rsbp holds is 32.7 degrees, 44
．． 2 degrees, 55.6 degrees, and 58.5 degrees.

Therefore, the angle of incidence that simultaneously satisfies RS"Rsbs and Rp"Rsbp is 44.2 degrees, which provides a singular angle of incidence. Therefore, an angle other than this singular angle of incidence may be determined as the measurement angle of incidence.

As described above, when implementing the present invention to measure the refractive index and film thickness of a thin film, it is sufficient to specify the singular angle of incidence and determine an angle other than the singular angle of incidence as the measurement incidence angle. In principle, the measurement angle of incidence can be freely selected as long as it is other than the singular angle of incidence, but if an angle that is too close to the singular angle of incidence is selected as the measurement incidence angle, the accuracy for measuring the refractive index and film thickness may not be sufficient. I can't get it. Therefore, the relationship between the difference between the singular angle of incidence and the measured angle of incidence and the measurement accuracy of refractive index and film thickness will be explained below, taking as an example the case where the refractive index of a single layer film is determined by the PRETTI method.

As an example, consider the following three samples based on FIG.

Sample J1: no=1.000. nl”1.46
0. dt=5000 people, n: 3.858-0.018
i sump/L/2: n6=1.000. n,=1.4
60. d,=10000J, n,'=3.858-0.
018i Sample 3: no=1.000. nt”1.480
．． dt” 20,000 people, n: 3.858-0.018
i Assume that the incident light is He-Ne laser light with a wavelength of 6328A.

When the energy reflectance Rs (6 degrees) for S-polarized light when this light is incident on the sample 1 is calculated as a function of the incident angle (0 to 90 degrees), it becomes as shown by the solid line in FIG. Further, when the energy reflectance 1 rozs(ao) 2 when directly incident on the substrate is calculated, it becomes as shown by the broken line in FIG.

Looking at this diagram, Rs (θa): I ro2s (flo)
l 2 holds true for θ. =46.7 degrees. Therefore, the energy reflectance Rp (6°) and Rs (a0) of P-polarized light and S-polarized light are calculated at an incident angle of 30° to 60° around 46.7°. In real situations, these are given as actual measurements. PR using this calculation result
The refractive index of the thin film was calculated by the ETTI method, and the ratio of the difference between the obtained refractive index value and the true value of 1.460 to the true value is shown in FIG.

Rs(ao) and l r0 calculated for sample 2
2; (ao) + 2 are shown in FIG. 9 by solid lines and broken lines, respectively.

Rs(llo) □ l rows(flo) l 2 holds true, the angle before and after θ = 46.7 degrees is 60 from 30 degrees
The energy reflectance R of P and S polarization at angles of incidence up to
Calculate p(θ0) and Rs(θ0), use the calculation results to calculate the refractive index of the thin film using the PRETTI method, and calculate the ratio of the difference between the obtained refractive index value and the true value of 1.460 to the true value. 1st
Shown in Figure 0.

Rs(θ0) and l r0 calculated for sample 3
2s(ao)12 are shown in FIG. 11 by solid lines and broken lines, respectively.

Rs(8o)" l ro2s(θ0)!" holds true, the angle of incidence from 30 degrees to 60 degrees, including the first two of θ0 = 18.9 degrees, 46.7 degrees, and 72.1 degrees. The energy reflectance Rp(θ0) and Rs of P-polarized light and S-polarized light are
(θ0), and using the calculation results, calculate the refractive index of the thin film using the PRETTI method, and the obtained refractive index value and true value 1.4
The ratio of the difference from 60 to the true value is shown in FIG.

Here, if m in equation (8) is called the order of the singular angle of incidence, the order that gives a singular angle of incidence of 46.7 degrees for samples 1 to 3 is m = 2 for sample 1 and m = 2 for sample 2. For sample 3, m=4, and for sample 3, m=:8. Referring to Figure 8.10.12, in all samples, each graph is a δ function type graph that diverges for a singular angle of incidence of 46.7 degrees, but the above order m is large. As the distance increases, the width of the divergent portion becomes narrower. and the singular angle of incidence θ,. , the range of incidence angle of 6° is approximately L+56-o-(9015m), 6o≧6. o+(9
015m) (angle unit degree), the accuracy of the refractive index obtained is within 0.1%.

Therefore, once the singular angle of incidence is determined, highly accurate measurement can be achieved by setting the measurement incidence angle in an incident angle region that satisfies the inequality (ILr'). For example, in the case of sample 3, the singular angle of incidence is given by the order m=8, so the angle of incidence region that provides refractive index measurement accuracy within 0.1% is (lI
+) to θ. ≦44.5 degrees and θ0≧48.95 degrees, so it is sufficient to set the measurement incident angle within this region, but 18
．． In the vicinity of 9 degrees and 72.1 degrees, the accuracy deteriorates due to the influence of singular angles of incidence of different orders, so measure within the range of (11+) above and where there is no influence of singular angles of incidence of other orders. It is better to set the angle of incidence.

Example 3 Finally, a specific example for measuring the refractive index and film thickness of a single layer film will be described.

As the substrate 10, complex refractive index nH=3.858-0.01
Measurement sample 0 is a Si substrate with a 81 diaphragm, on which a SiO □ film is provided as a thin film 12 by thermal oxidation.
It is installed on the turntable 6 shown in FIG. 13, and the incident angle is θ. was continuously changed from 10 to 80 degrees, and the photoelectric conversion output of the photodetector 4.5 was taken into the data processing system 8 at 0.1 degree increments of the incident angle. Then, the energy reflectance Rs (θ0) of S-polarized light in the above incident angle region was measured in 0°/1° increments. This result is shown in FIG. 14 as a solid line. Reflectance 1 when S-polarized light is directly incident on the substrate at the same incident angle
The result of calculating r02s(θ0)12 is shown in FIG. 14 by a broken line.

As is clear from FIG. 14, the equation Rs(θ0)=
ro,,s(θ)Hz holds true for θ. =28.7 degrees, which is the singular angle of incidence. Therefore, the measurement incident angle was determined to be 50.0 degrees, and the measurement incident angle to the sample O was set. Next, the energy reflectance of S-polarized light and P-polarized light with respect to this measured incident angle was measured using a set of polarizer 3, and the following results were obtained.

Rs(50,0@)=0.0991452. Rp(50
,0')=0.127581 Using these values, PR
When the refractive index of the SiO□ thin film is determined by the ETTI method, n:
It became 1.459.

The measured value (Φ23P-Φ23g) of (Φ23P-Φ23,) calculated for calculating the refractive index and the calculated value (Φ23
F-Φ23g)C is shown in FIG. 15, and the refractive index of the thin film is varied from 1.35 to 1.55.

In the PRETTI method, (Φ21.-Φ23g)m and (Φ2
31. -φ238) The more clearly the graphs of C intersect, the better the accuracy is.As is clear from Figure 15, both graphs clearly intersect at n=1.459, so the accuracy of the obtained refractive index is high. .

Further, the above measurement sample was set in an ellipsometer, and the refractive index and film thickness were measured by ellipsometry at an incident angle of 50.0°. As a result, the refractive index n was 1.459 and the film thickness d was 9117.

The specific angle of incidence for this measurement sample is 26.
It is 7 degrees. Therefore, a psi-delta diagram of the above measurement sample in ellipsometry is shown in FIG. 1.4 to n
59. At the point of d+=9117, graphs with different refractive indexes are crowded, as shown by the X mark, and it can be seen that this is an area where it is actually extremely difficult to determine the refractive index. It can thus be seen that, in principle, the refractive index and film thickness of a thin film cannot be determined even with ellipsometry at a singular angle of incidence.

[Effects of the Invention] As described above, according to the present invention, a novel method for determining the angle of incidence in measuring the refractive index and thickness of a thin film can be provided.

Since this method has the above-described configuration, it is possible to easily and reliably determine the measurement incident angle that provides good measurement accuracy when measuring the refractive index and film thickness of a thin film.

[Brief explanation of the drawing]

FIG. 1 is a diagram for explaining the invention of claim 1, FIGS. 2 and 3 are diagrams for explaining the invention in detail of claim 1, and FIG. 4 is a diagram for explaining the invention of claim 2. FIGS. 5 and 6 are diagrams for explaining the invention of claim 2 in detail, and FIGS. 7 to 12 are diagrams showing the relationship between the measurement incident angle and the accuracy of refractive index measurement. FIG. 13 is a diagram for explaining the relationship, FIG. 13 is a diagram showing the main parts of the apparatus for carrying out the embodiment, and FIGS. FIG. 3 is a diagram for explaining an example applied to thickness measurement. 10.20. ,,substrate, 12.22-1. ,, thin film (its refractive index and film thickness are the objects of measurement), 22-1.22-
2. , , ,22-n+0. . Even? Fig. 1) Reflectance dependent on input level (e-polarized light) 1. Structure of intestine gω (*1 order) 1. Structure of 5. (rrL layer order) 1. Porridge

Claims (1)

[Claims] 1. When measuring the refractive index and film thickness of a single-layer thin film formed on a substrate having a known complex refractive index n^*_2=2-ik_2, monochromatic light for measurement is used. A method for determining the measurement incident angle, the method comprising: determining various incident angles θ_0 of monochromatic light of wavelength λ used for measurement;
While measuring the energy reflectance Rs (θ_0) or Rp (θ_0) of S-polarized light or P-polarized light by the measurement sample for Or the energy reflectance of P-polarized light |r0_2_s(θ_0)|^2 or |r_0_
2_s(θ_0)|^2 is calculated as a function of the incident angle θ_0 using the above n^*_2, n_0, and the equation Rs(θ_0)=|r_0_2_s(θ_0)|^2 or Rp(θ_0)= A method for determining an incident angle in refractive index/film thickness measurement, characterized by determining an angle θ_a_0 that satisfies |r_0_2_p(θ_0)|^2, and setting an angle other than this θ_a_0 as a measurement incident angle. 2. Refractive index/film of a thin film formed on a substrate formed by laminating one or more thin films with a known refractive index and film thickness on a substrate having a known complex refractive index n^*_a=n_a−ik_a A method of determining the measurement incident angle of monochromatic light for measurement when measuring thickness, the method comprising: determining the measurement incident angle of monochromatic light of wavelength λ used for measurement at various incident angles θ_0
While measuring the energy reflectances Rs(θ_0) and Rp(θ_0) of S-polarized light and P-polarized light by the measurement sample, the S-polarized light and Energy reflectance of P-polarized light R_s_b_s(θ_0) and R_s_b_p(θ_
0) is calculated as a function of the incident angle θ_0 using the above n^*_a, n_0 and the known refractive index and film thickness of each thin film of the substrate, and the equation Rs(θ_0)=R_s_b_s(θ_0) and Rp( A method for determining an incident angle in refractive index/film thickness measurement, characterized by determining an angle θ_a_0 that simultaneously satisfies θ_0)=R_s_b_p(θ_0), and setting an angle other than θ_a_0 as a measurement incident angle.